It is proved that the Cartesian product of an odd cycle with the complete graph on 2 vertices, is determined by the spectrum of the adjacency matrix. We also present some computational results on the spectral characterization of cubic graphs on at most 20 vertices.
Let G be a graph of order n and let µ be an eigenvalue of multiplicity m. A star complement for µ in G is an induced subgraph of G of order n − m with no eigenvalue µ. In this paper, we study maximal and regular graphs which have K r,s + tK 1 as a star complement for 1 as the second largest eigenvalue. It turns out that some well known strongly regular… (More)